Question: The grades on a language midterm at Gardner Bullis are normally distributed with $\mu = 66$ and $\sigma = 4.5$. Vanessa earned a $68$ on the exam. Find the z-score for Vanessa's exam grade. Round to two decimal places.
A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Vanessa's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{68 - {66}}{{4.5}}} $ ${ z \approx 0.44}$ The z-score is $0.44$. In other words, Vanessa's score was $0.44$ standard deviations above the mean.